Mathematica Bohemica, Vol. 145, No. 2, pp. 127-140, 2020
Some module cohomological properties of Banach algebras
Elham Ilka, Amin Mahmoodi, Abasalt Bodaghi
Received June 3, 2017. Published online March 25, 2019.
Abstract: We find some relations between module biprojectivity and module biflatness of Banach algebras $\mathcal A$ and $\mathcal B$ and their projective tensor product $\mathcal A \mathbin{\widehatøtimes}\mathcal B$. For some semigroups $S$, we study module biprojectivity and module biflatness of semigroup algebras $l^1(S)$.
References: [1] M. Amini: Module amenability for semigroup algebras. Semigroup Forum 69 (2004), 243-254; Corrigendum ibid. 72 (2006), page 493. DOI 10.1007/s00233-004-0107-3 | MR 2081295 | Zbl 1059.43001
[2] M. Amini, A. Bodaghi, D. Ebrahimi Bagha: Module amenability of the second dual and module topological center of semigroup algebras. Semigroup Forum 80 (2010), 302-312. DOI 10.1007/s00233-010-9211-8 | MR 2601766 | Zbl 1200.43001
[3] A. Bodaghi: Module amenability of the projective module tensor product. Malay. J. Math. Sci. 52 (2011), 257-265. MR 2854379 | Zbl 1254.46051
[4] A. Bodaghi, M. Amini: Module character amenability of Banach algebras. Arch. Math. 99 (2012), 353-365. DOI 10.1007/s00013-012-0430-y | MR 2990154 | Zbl 1267.46062
[5] A. Bodaghi, M. Amini: Module biprojective and module biflat Banach algebras. Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 75 (2014), 25-36. MR 3130203 | Zbl 1299.43002
[6] A. Bodaghi, M. Amini, R. Babaee: Module derivations into iterated dual of Banach algebras. Proc. Rom. Acad., Ser. A, Math. Phys. Tech. Sci. Inf. Sci. 12 (2011), 277-284. MR 2870494 | Zbl 1324.46060
[7] A. Bodaghi, H. Ebrahimi, M. Lashkarizaheh Bami: Generalized notions of module character amenability. Filomat 31 (2017), 1639-1654. DOI 10.2298/FIL1706639B | MR 3635202
[8] A. Bodaghi, A. Jabbari: Module biflatness of the second dual of Banach algebras. Math. Rep., Buchar. 17 (2015), 235-247. MR 3375731 | Zbl 1374.46038
[9] H. G. Dales: Banach Algebras and Automatic Continuity. London Mathematical Society Monographs. New Series 24. Oxford University Press, Oxford (2000). MR 1816726 | Zbl 0981.46043
[10] J. Duncan, I. Namioka: Amenability of inverse semigroups and their semigroup algebras. Proc. R. Soc. Edinb., Sect. A 80 (1978), 309-321. DOI 10.1017/S0308210500010313 | MR 0516230 | Zbl 0393.22004
[11] M. Essmaili, A. R. Medghalchi: Biflatness of certain semigroup algebras. Bull. Iran. Math. Soc. 39 (2013), 959-969. MR 3126267 | Zbl 1300.43005
[12] N. Grønbaek: Biflatness and biprojectivity of Banach algebras graded over a semilattice. Glasg. Math. J. 52 (2010), 479-495. DOI 10.1017/S0017089510000364 | MR 2679908 | Zbl 1210.46037
[13] H. İnceboz, B. Arslan, A. Bodaghi: Module symmetrically amenable Banach algebra. Acta Math. Acad. Paedagog. Nyházi. (N.S.) 33 (2017), 233-245.
[14] B. E. Johnson: Cohomology in Banach Algebras. Memoirs of the American Mathematical Society 127. AMS, Providence (1972). DOI 10.1090/memo/0127 | MR 0374934 | Zbl 0256.18014
[15] A. Ya. Khelemskij: Flat Banach modules and amenable algebras. Trudy Moskov. Mat. Obshch. 47 (1984), 179-218 (In Russian.). MR 0774950 | Zbl 0569.46027
[16] M. Lashkarizadeh Bami, M. Valaei, M. Amini: Super module amenability of inverse semigroup algebras. Semigroup Forum 86 (2013), 279-288. DOI 10.1007/s00233-012-9432-0 | MR 3034775 | Zbl 1277.46022
[17] H. Pourmahmood-Aghababa: (Super) module amenability, module topological center and semigroup algebras. Semigroup Forum 81 (2010), 344-356. DOI 10.1007/s00233-010-9231-4 | MR 2678721 | Zbl 1207.46039
[18] H. Pourmahmood-Aghababa: A note on two equivalence relations on inverse semigroups. Semigroup Forum 84 (2012), 200-202. DOI 10.1007/s00233-011-9365-z | MR 2886007 | Zbl 1242.20070
[19] H. Pourmahmood-Aghbaba, A. Bodaghi: Module approximate amenability of Banach algebras. Bull. Iran. Math. Soc. 39 (2013), 1137-1158. MR 3145209 | Zbl 1301.43002
[20] P. Ramsden: Biflatness of semigroup algebras. Semigroup Forum. 79 (2009), 515-530. DOI 10.1007/s00233-009-9169-6 | MR 2564061 | Zbl 1213.43002
[21] R. Rezavand, M. Amini, M. H. Sattari, D. Ebrahimi Bagha: Module Arens regularity for semigroup algebras. Semigroup Forum 77 (2008), 300-305; Corrigendum 79 (2009), 214-215. DOI 10.1007/s00233-008-9075-3 | MR 2443440 | Zbl 1161.46026
[22] M. A. Rieffel: Induced Banach representations of Banach algebras and locally compact groups. J. Func. Anal. 1 (1967), 443-491. DOI 10.1016/0022-1236(67)90012-2 | MR 0223496 | Zbl 0181.41303
Affiliations: Elham Ilka, Amin Mahmoodi, Department of Mathematics, Central Tehran Branch, Islamic Azad University, Pounak Square, Imam Hasan Street, 14696-99191 Tehran, Iran, e-mail: elh.ilka.sci@iauctb.ac.ir, a_mahmoodi@iauctb.ac.ir; Abasalt Bodaghi, Department of Mathematics, Garmsar Branch, Islamic Azad University, Daneshjoo Street, 35816-31167 Garmsar, Iran, e-mail: abasalt.bodaghi@gmail.com
